Duration:
Number of lectures per week: 3

Assessment: Assignments counting 10%

End-of-year Examination: One three hour examination

Description:

1. The Principle of Mathematical Induction.

2. Sets and functions: power sets; binary relations; congruences; equivalence relations; partial orders and lattices; Cartesian products; functions between sets; inverse functions; injective, surjective and bijective functions; partial mappings.

3. Graphs: incidence and adjacency matrices, complete graphs, bipartite graphs; connectedness and components; Euler trails; Hamilton paths; forests and trees; directed graphs.

4. Algebraic structures: semigroups, monoids and groups; homomorphisms and isomorphisms.

5. Grammars: phrase structure and Chomsky hierarchy; Languages: context free and regular; Machines: finite state acceptors

6. Ordinary Differential Equations: higher order, initial and boundary value problems

7. Fourier Series: orthonormal functions, Euler coefficients, half-range expansions, truncated series approximation.

Textbooks:

1. M. Piff, Discrete Mathematics, Cambridge University Press.

2. Judith L. Gersting, Mathematical Structures for Computer Science, W. H. Freeman.

3. D. J. Cooke & H. E. Bez, Computer Mathematics, Cambridge University Press.

4. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Addison-Wesley.

5. W. E. Boyce & R. C. DiPrima, Elementary Differential Equations, John Wiley.

Nov 8, 2000